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Conclusions and Discussion
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For the dam-break hydrographs considered and the range of channel slopes modeled, the simple diffusion dam-break model of equation 12 provides estimates of flood depths and outflow hydrographs which compare favorably to the results determined by the well-known K-634 one-dimensional dam-break model. Generally speaking, the difference between the two modeling approaches is found to be less than a 3 percent variation in predicted flood depths.
The presented diffusion dam-break model is based upon a straightforward explicit timestepping method which allows the model to operate upon the nodal points without the need to use large matrix systems. Consequently, the model can be implemented on most currently available microcomputers. However, as compared to implicit solution methods, time steps for DHM use are extremely small. Thus, relatively short simulation times must be used.
The diffusion model of equation 22 can be directly extended to a two-dimensional model by adding the y-direction terms which are computed in a similar fashion as the x-direction terms. The resulting two-dimensional diffusion model is texted by modeling the considered test problems in the x-direction, the y-direction, and along a 45-degree trajectory across a two-dimensional grid aligned with the x-y coordinate axis. Using a similar two-dimensional model, Xanthopoulos and Koutitas (1976) conceptually verify the diffusion modeling technique by considering the evolution of a two-dimensional flood plain which propagates radially from the dam-break site.
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